Question

There is a rectangular plate of mass $M\, kg$ of dimensions $( a \times b )$. The plate is held in horizontal position by striking n small balls each of mass $m$ per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$?

It is given $n=100, M=3 \,kg , m=0.01\, kg ; b=2\, m ; a=1$ $m ; g =10 \,m / s ^{2}$

Answer 1

Let $n$ be the number of balls striking the shaded part of the plate per unit area per unit time.
Taking $T$ about the hinged end, we get
$n (2 mv ) \times\left(\frac{a b}{2}\right) \times \frac{3 b}{4}= Mg \frac{b}{2}$
Therefore,
$v =\frac{2 Mg }{2 mmab }$
$=\frac{2}{3} \times \frac{3 \times 10}{100 \times 0.01 \times 2}=10\, m / s$